Fig.REF  presents the critical behavior of \(T/T_c -S/S_c\)  in the Taub NUT black hole for \(\hat{n} = 0.05, 0.5, 1, 2\)  with different \(q=0.6, 1, 1.5\) , separately. From the figure, we find that for \(q<1\) , there is a critical point in \(n=0.5\) . Also, \(\hat{n}\le 0.13\)  is more suitable for the Taub-NUT-AdS black holes at the critical point in \(RPS\)  formalism. Also, in the limit of \(\hat{n}\rightarrow 0\) , the diagrams recover the results in [1]}, [2]}.
